First off, there is really no 'correct' way to make vegetable beef soup, other than having a few veggies on hand to throw into a pot or slow cooker. Obviously, having some chunks of beef cut up into bite-sized pieces would be nice also. Other items that are required (for my version of this soup anyway), is a can of petite diced tomatoes, a carrot or two, a small potato, celery, green beans, corn some spices and a cup and a half of water. The only precooking required is to braise the beef chunks in a medium hot skillet for a few minutes.
Otherwise, just cut every thing into small pieces and dump it all into the slow cooker. For the spices, I like to use Lite Salt (50% fake salt), pepper and a smidgeon of cayenne pepper for some added bite. I add all these at the same time, replace the lid on the slow cooker, set it on high for three hours and then reduce the heat to the low setting for another three. Voila! Soups on!
That's all there is to it! Other than to go and enjoy the soup, that is!